Abstract

In this paper, we describe a skeletonization method effective and robust when applied to complex shapes, even if affected by boundary perturbations. This approach has been applied to binary segmented images containing bi-dimensional bounded shapes, generally not simply connected. It has been considered an external force field derived by an anisotropic flow. Through the divergence, we have examined the field flow at different times, discovering that the field divergence satisfies an anisotropic diffusion equation as well. Curves of positive divergence may be thought as propagating fronts converging to a steady state formed by shocks points. It has been proved that the sets of points, inside the shape, where divergence assumes positive values, converge to the skeleton. The curves with negative values of divergence remain static, so they may be directly used for edge extraction. This methodology has also been tested respect to boundary perturbations and disconnections.

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Several computational approaches have been implemented during the last decades for skeleton extraction. Skeletonization provides an effective and compact representation reducing a 3D form to a surface and a 2D form to a one-dimensional structure. There are different classes of methods to compute skeleton of bounded objects. Methods based on Distance Transform (DT) generate a distance map, a graylevel image representing the distance to the closest boundary from each point of the shape. In this framework, the skeleton is described as being the locus of local maxima of a distance map (Blum,1967), (Montanari,1969). If this function is visualized in the three-dimensional space it appears as a not differentiable surface showing ridges formed by points that, when projected onto the image plane, define the skeleton structure. The topological thinning methods work eroding iteratively the shape until the skeleton is obtained (Ammann & Sartori-Angus, 1985), (Zhang & Wan, 1996).

In most cases the criteria used to delete a point are local, whereas the skeleton allows to capture global geometric features of a given shape (Pavlidis,1980, Lam, Lee & Suen,1992). Skeleton may be computed by Voronoi diagrams created using boundary points as anchor points (Ogniewicz, & Ilg, 1992). The main drawback of this approach is that a great number of anchor points are not relevant for skeleton generation and therefore additional skeleton branches are frequently introduced. The Field-based approaches evaluate skeletons recurring to potential functions, derived by the Electrostatic or Gravitational Theory. Boundary pixels are considered behaving like point sources of a potential field, as a consequence these methods require a reliable contour point localization. The resulting fields are diffused introducing an edge-strength function. In this context the skeleton is extracted through the level curves of the strength function (Grigorishin, Abdel-Hamid, & Yang, 1996).